Since my first axie suddenly died (and I had no idea why until I did some research after) I've been more vigilant looking for signs of illness. I'm still fairly new at this, so I also draw on my experience with fish and reptiles. Here's what I believe to be *possible* signs of stress or illness:
Gills:
- tilted forward (too much water flow)
- losing "fluffiness" (fine filaments)
- curling at the ends - I've seen pics of many axies with curled gills, so I'm not 100% sure if this is anything to worry about. My axie who died developed curled gills within the last week before she died.
- pieces missing, especially from the thicker bits
- whitish fuzz on gills
- extremely pale (not just when they're resting/asleep)
- axolotl gulping a lot of air at the surface (may mean lack of oxygen)
Skin
- white patches, mucus (can be sign of heat stress)
- fuzzy patches
- red patches, look like wounds (could be physical damage or infection)
- wounds
Limbs
- missing, damageds
- "red leg" bacterial infection
- axie not moving them normally, limb(s) may be dangling or curled backwards
Tail
- stays curled at the end
- fin looks ragged, curled, may look reddish or whitish
- chunks of fin missing, torn
Behaviour
- refusal to eat
- doesn't poop
- gulps air at the surface a lot
- floats at the surface AND tries to get back down, but can't
- looks bloated, may also float or tilt to one side
- lethargic, hides all the time and doesn't move much
Those are the things I watch for. They aren't necessarily emergencies, but something to keep an eye on. I'm sure others will be able to think of more symptoms.